Structure of the Hamiltonian of mean force

The Hamiltonian of mean force is an effective Hamiltonian that allows a quantum system, nonweakly coupled to an environment, to be written in an effective Gibbs state. We present results on the structure of the Hamiltonian of mean force in extended quantum systems with local interactions. We show that its spatial structure exhibits a "skin effect"-its difference from the system Hamiltonian dies off exponentially with distance from the system-environment boundary. For spin systems, we identify the terms that can appear in the Hamiltonian of mean force at different orders in the inverse temperature.